f(x)=1/square root of x and g(x)=x^2-4 state the domains for each of the following using interval notation Domain of g(f(x))

Question

f(x)=1/square root of x and g(x)=x^2-4 state the domains for each of the following using interval

notation

Domain of g(f(x))=

Answer 1

f(x) = 1/sqrx x> 0

g(x)= x^2 -4

g(f(x)) = (1/sqrx)^2 -4

g(f(x)) = 1/x -4

domain of f(x) is x>0, x is in the interval (0, infinity)

domain of g(x) is all real numbers (-infinity, infinity)

domain of g(f(x)) is all real numbers except x=0, (-infinity,0) U (0, infinity)